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• W2892373386 abstract "Given a consequence relation in many-valued logic, what connectives can be defined? For instance, does there always exist a conditional operator internalizing the consequence relation, and which form should it take? In this paper, we pose this question in a multi-premise multi-conclusion setting for the class of so-called intersective mixed consequence relations, which extends the class of Tarskian relations. Using computer-aided methods, we answer extensively for 3-valued and 4-valued logics, focusing not only on conditional operators, but on what we call Gentzen-regular connectives (including negation, conjunction, and disjunction). For arbitrary N-valued logics, we state necessary and sufficient conditions for the existence of such connectives in a multi-premise multi-conclusion setting. The results show that mixed consequence relations admit all classical connectives, and among them pure consequence relations are those that admit no other Gentzen-regular connectives. Conditionals can also be found for a broader class of intersective mixed consequence relations, but with the exclusion of order-theoretic consequence relations." @default.
• W2892373386 created "2018-09-27" @default.
• W2892373386 creator A5078417903 @default.
• W2892373386 creator A5090078698 @default.
• W2892373386 date "2018-09-04" @default.
• W2892373386 modified "2023-09-25" @default.
• W2892373386 title "From Many-Valued Consequence to Many-Valued Connectives" @default.
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